Googology Wiki
Googology Wiki

EDIT: My first big milestone: 1000 edits! :))


My name is Binary198, and I like to create notations and powerful functions. I have been interested in googology, especially ordinals and large cardinals, for over a year as of now, and I'm glad I can finally share my contributions with the wider world. I have a Google large numbers site at, although it's been a long time since I did anything there. I use they/them pronouns.

Name: Binary198

Country: UK

Time zone: UTC

Personality Type: INTJ-T

I published most of my old stuff on my website. Nowadays however, it is mostly inactive. I publish most of my new things on my user blog. Below are some of my user pages.


User:Binary198/Binary Stability Theory - Another theory which works with predicates, this time taking a more \(Z_2\)-like approach. It is weaker than elementary stability theory, but still likely stronger than ZFC.

User:Binary198/Elementary Stability Theory - A theory whose domain of discourse is the class of predicates. I conjecture it to be stronger than \(n\)th-order arithmetic for all finite \(n\).

User:Binary198/Large cardinals - A compilation of large cardinal properties that I made or I like. I actually studied large cardinals for 1 or 2 years before I joined the Googology community.

User:Binary198/Oracles - My attempt to construct a new super-powerful language based on oracle machines.

User:Binary198/OCFs - A collection of ordinal collapsing functions.


User:Binary198/Formalized UNOCF - A terrible attempt to formalize UNOCF.

User:Binary198/Introduction and analysis of GAN/BINAN - My array notation, which my educated guesses believe to have level \(\geq \psi_\Omega(\chi_M(0))\), although no formal analysis has been conducted beyond \(\varphi(\omega, 0)\). Discontinued because I got bored and it was really unoriginal and ill-defined.

User:Binary198/TMOAN - My so-called "mini OCF", which uses infinite ordinals to generate large numbers, like FGH. It is inactive, but I might fix it sometime soon.